Effect of the conditional scalar dissipation rate in the conditional moment closure

In turbulent premixed flames, for the mixing at a molecular level of reactants and products on the flame surface, it is crucial to sustain the combustion. This mixing phenomenon is featured by the scalar dissipation rate, which may be broadly defined as the rate of micro-mixing at small scales. This term, which appears in many turbulent combustion methods, includes the Conditional Moment Closure (CMC) and the Probability Density Function (PDF), requires an accurate model. In this study, a mathematical closure for the conditional mean scalar dissipation rate, <Nc|ζ>, in Reynolds, Averaged Navier–Stokes (RANS) context is proposed and tested against two different Direct Numerical Simulation (DNS) databases having different thermochemical and turbulence conditions. These databases consist of lean turbulent premixed V-flames of the CH4-air mixture and stoichiometric turbulent premixed flames of H2-air. The mathematical model has successfully predicted the peak and the typical profile of <Nc|ζ> with the sample space ζ and its prediction was consistent with an earlier study.

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Modeling an Enclosed, Turbulent Reacting Methane Jet With the Premixed Conditional Moment Closure Method

Volume 1B: Combustion, Fuels and Emissions ◽

10.1115/gt2013-95092 ◽

2013 ◽

Cited By ~ 4

Author(s):

Scott Martin ◽

Aleksandar Jemcov ◽

Björn de Ruijter

Keyword(s):

Turbulent Combustion ◽

Large Scale ◽

Reaction Rates ◽

Moment Closure ◽

Scalar Dissipation ◽

Small Scale ◽

Conditional Moment ◽

Progress Variable ◽

Conditional Moment Closure ◽

Scale Turbulence

Here the premixed Conditional Moment Closure (CMC) method is used to model the recent PIV and Raman turbulent, enclosed reacting methane jet data from DLR Stuttgart [1]. The experimental data has a rectangular test section at atmospheric pressure and temperature with a single inlet jet. A jet velocity of 90 m/s is used with an adiabatic flame temperature of 2,064 K. Contours of major species, temperature and velocities along with velocity rms values are provided. The conditional moment closure model has been shown to provide the capability to model turbulent, premixed methane flames with detailed chemistry and reasonable runtimes [2]. The simplified CMC model used here falls into the class of table lookup turbulent combustion models where the chemical kinetics are solved offline over a range of conditions and stored in a table that is accessed by the CFD code. Most table lookup models are based on the laminar 1-D flamelet equations, which assume the small scale turbulence does not affect the reaction rates, only the large scale turbulence has an effect on the reaction rates. The CMC model is derived from first principles to account for the effects of small scale turbulence on the reaction rates, as well as the effects of the large scale mixing, making it more versatile than other models. This is accomplished by conditioning the scalars with the reaction progress variable. By conditioning the scalars and accounting for the small scale mixing, the effects of turbulent fluctuations of the temperature on the reaction rates are more accurately modeled. The scalar dissipation is used to account for the effects of the small scale mixing on the reaction rates. The original premixed CMC model used a constant value of scalar dissipation, here the scalar dissipation is conditioned by the reaction progress variable. The steady RANS 3-D version of the open source CFD code OpenFOAM is used. Velocity, temperature and species are compared to the experimental data. Once validated, this CFD turbulent combustion model will have great utility for designing lean premixed gas turbine combustors.

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A-Priori Validation of Scalar Dissipation Rate Models for Turbulent Non-Premixed Flames

Flow Turbulence and Combustion ◽

10.1007/s10494-020-00218-x ◽

2020 ◽

Author(s):

M. P. Sitte ◽

C. Turquand d’Auzay ◽

A. Giusti ◽

E. Mastorakos ◽

N. Chakraborty

Keyword(s):

Dissipation Rate ◽

A Priori ◽

Turbulent Flames ◽

Large Eddy Simulations ◽

Moment Closure ◽

Scalar Dissipation ◽

Combustion Model ◽

Scalar Dissipation Rate ◽

Jet Flame ◽

Large Eddy

Abstract The modelling of scalar dissipation rate in conditional methods for large-eddy simulations is investigated based on a priori direct numerical simulation analysis using a dataset representing an igniting non-premixed planar jet flame. The main objective is to provide a comprehensive assessment of models typically used for large-eddy simulations of non-premixed turbulent flames with the Conditional Moment Closure combustion model. The linear relaxation model gives a good estimate of the Favre-filtered scalar dissipation rate throughout the ignition with a value of the related constant close to the one deduced from theoretical arguments. Such value of the constant is one order of magnitude higher than typical values used in Reynolds-averaged approaches. The amplitude mapping closure model provides a satisfactory estimate of the conditionally filtered scalar dissipation rate even in flows characterised by shear driven turbulence and strong density variation.

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Large Eddy Simulation of an Enclosed Turbulent Reacting Methane Jet With the Tabulated Premixed Conditional Moment Closure Method

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4032846 ◽

2016 ◽

Vol 138 (10) ◽

Cited By ~ 6

Author(s):

Carlos Velez ◽

Scott Martin ◽

Aleksander Jemcov ◽

Subith Vasu

Keyword(s):

Turbulent Combustion ◽

Moment Closure ◽

Scalar Dissipation ◽

Combustion Model ◽

Conditional Moment ◽

Eddy Simulation ◽

Conditional Moment Closure ◽

Major Species ◽

Large Eddy ◽

Closure Method

The tabulated premixed conditional moment closure (T-PCMC) method has been shown to provide the capability to model turbulent, premixed methane flames with detailed chemistry and reasonable runtimes in Reynolds-averaged Navier–Stokes (RANS) environment by Martin et al. (2013, “Modeling an Enclosed, Turbulent Reacting Methane Jet With the Premixed Conditional Moment Closure Method,” ASME Paper No. GT2013-95092). Here, the premixed conditional moment closure (PCMC) method is extended to large eddy simulation (LES). The new model is validated with the turbulent, enclosed reacting methane backward facing step data from El Banhawy et al. (1983, “Premixed, Turbulent Combustion of a Sudden-Expansion Flow,” Combust. Flame, 50, pp. 153–165). The experimental data have a rectangular test section at atmospheric pressure and temperature with an inlet velocity of 10.5 m/s and an equivalence ratio of 0.9 for two different step heights. Contours of major species, velocity, and temperature are provided. The T-PCMC model falls into the class of table lookup turbulent combustion models in which the combustion model is solved offline over a range of conditions and stored in a table that is accessed by the computational fluid dynamic (CFD) code using three controlling variables: the reaction progress variable (RPV), variance, and local scalar dissipation rate. The local scalar dissipation rate is used to account for the affects of the small-scale mixing on the reaction rates. A presumed shape beta function probability density function (PDF) is used to account for the effects of subgrid scale (SGS) turbulence on the reactions. SGS models are incorporated for the scalar dissipation and variance. The open source CFD code OpenFOAM is used with the compressible Smagorinsky LES model. Velocity, temperature, and major species are compared to the experimental data. Once validated, this low “runtime” CFD turbulent combustion model will have great utility for designing the next generation of lean premixed (LPM) gas turbine combustors.

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IMPLEMENTATION OF THE CONDITIONAL MOMENT CLOSURE MODEL TO A TURBULENT NONPREMIXED H2/CO-AIR FLAME STABILIZED ON A BLUFF BODY

Transactions of the Canadian Society for Mechanical Engineering ◽

10.1139/tcsme-1999-0028 ◽

1999 ◽

Vol 23 (3-4) ◽

pp. 425-433 ◽

Cited By ~ 2

Author(s):

S.- H. Kim ◽

T. Liu ◽

K.Y. Huh

Keyword(s):

Bluff Body ◽

Reaction Rates ◽

Moment Closure ◽

Scalar Dissipation ◽

Conditional Moment ◽

Turbulent Diffusion Flame ◽

Recirculating Flow ◽

Conditional Moment Closure ◽

Mass Fractions ◽

Turbulent Nonpremixed

A turbulent nonpremixed flame of H2/CO-air stabilized on a bluff-body is simulated by the conditional moment closure (CMC) model. Full spatial variation of the conditional quantities is taken into account for an elliptic recirculating flow field. Comparison has shown reasonable agreement for the conditional and Favre mean temperature and mass fractions of CO and H20 between calculation and experiment. Overprediction of the peak OH mass fraction is attributed to inaccurate modelling of the conditional scalar dissipation rate. The CMC model is capable of predicting major features of a turbulent diffusion flame characterized by finite chemical reaction rates.

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Conditional Moment Closure Modelling of a Lifted H2/N2Turbulent Jet Flame Using the Presumed Mapping Function Approach

Journal of Combustion ◽

10.1155/2015/257145 ◽

2015 ◽

Vol 2015 ◽

pp. 1-24

Author(s):

Ahmad El Sayed ◽

Roydon A. Fraser

Keyword(s):

Mixture Fraction ◽

Mapping Function ◽

Moment Closure ◽

Scalar Dissipation ◽

Conditional Moment ◽

Jet Flame ◽

Velocity Statistics ◽

Conditional Moment Closure ◽

Consistent Manner ◽

Radical History

A lifted hydrogen/nitrogen turbulent jet flame issuing into a vitiated coflow is investigated using the conditional moment closure (CMC) supplemented by the presumed mapping function (PMF) approach for the modelling of conditional mixing and velocity statistics. Using a prescribed reference field, the PMF approach yields a presumed probability density function (PDF) for the mixture fraction, which is then used in closing the conditional scalar dissipation rate (CSDR) and conditional velocity in a fully consistent manner. These closures are applied to a lifted flame and the findings are compared to previous results obtained usingβ-PDF-based closures over a range of coflow temperatures (Tc). The PMF results are in line with those of theβ-PDF and compare well to measurements. The transport budgets in mixture fraction and physical spaces and the radical history ahead of the stabilisation height indicate that the stabilisation mechanism is susceptible toTc. As in the previousβ-PDF calculations, autoignition around the “most reactive” mixture fraction remains the controlling mechanism for sufficiently highTc. Departure from theβ-PDF predictions is observed whenTcis decreased as PMF predicts stabilisation by means of premixed flame propagation. This conclusion is based on the observation that lean mixtures are heated by downstream burning mixtures in a preheat zone developing ahead of the stabilization height. The spurious sources, which stem from inconsistent CSDR modelling, are further investigated. The findings reveal that their effect is small but nonnegligible, most notably within the flame zone.

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LES Simulation of an Enclosed Turbulent Reacting Methane Jet With the Tabulated Premixed CMC Method

Volume 4B: Combustion, Fuels and Emissions ◽

10.1115/gt2015-43788 ◽

2015 ◽

Cited By ~ 1

Author(s):

Carlos Velez ◽

Scott Martin ◽

Aleksander Jemcov ◽

Subith Vasu

Keyword(s):

Experimental Data ◽

Turbulent Combustion ◽

Moment Closure ◽

Scalar Dissipation ◽

Combustion Model ◽

Small Scale ◽

Conditional Moment ◽

Conditional Moment Closure ◽

Major Species ◽

Closure Method

The Tabulated Premixed Conditional Moment Closure Method (T-PCMC) has been shown to provide the capability to model turbulent, premixed methane flames with detailed chemistry and reasonable runtimes in a RANS environment [1]. Here the premixed conditional moment closure method is extended to Large Eddy Simulation. The new model is validated with the turbulent, enclosed reacting methane backward facing step data from El Banhawy [2]. The experimental data has a rectangular test section at atmospheric pressure and temperature with an inlet velocity of 10.5 m/s and an equivalence ratio of 0.9 for two different step heights. Contours of major species, velocity and temperature are provided. The T-PCMC model falls into the class of table lookup turbulent combustion models where the combustion model is solved offline over a range of conditions and stored in a table that is accessed by the CFD code using three controlling variables; the reaction progress variable, variance and local scalar dissipation rate. The local scalar dissipation is used to account for the affects of the small scale mixing on the reaction rates. A presumed shape beta function PDF is used to account for the effects of large scale turbulence on the reactions. Sub-grid scale models are incorporated for the scalar dissipation and variance. The open source CFD code OpenFOAM is used with the compressible Smagorinsky LES model. Velocity, temperature and major species are compared to the experimental data. Once validated, this “low runtime” CFD turbulent combustion model will have great utility for designing the next generation of lean premixed gas turbine combustors.

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Consistent Conditional Moment Closure Modelling of a Lifted Turbulent Jet Flame Using the Presumedβ-PDF Approach

Journal of Combustion ◽

10.1155/2014/507459 ◽

2014 ◽

Vol 2014 ◽

pp. 1-25 ◽

Cited By ~ 3

Author(s):

Ahmad El Sayed ◽

Roydon A. Fraser

Keyword(s):

Mixture Fraction ◽

Turbulent Jet ◽

Moment Closure ◽

Scalar Dissipation ◽

Conditional Moment ◽

Jet Flame ◽

Gradient Diffusion ◽

Conditional Moment Closure ◽

History Of ◽

Closure Modelling

A liftedH2/N2turbulent jet flame issuing into a vitiated coflow is investigated using the conditional moment closure. The conditional velocity (CV) and the conditional scalar dissipation rate (CSDR) submodels are chosen such that they are fully consistent with the moments of the presumedβprobability density function (PDF). The CV is modelled using the PDF-gradient diffusion model. Two CSDR submodels based on the double integration of the homogeneous and inhomogeneous mixture fraction PDF transport equations are implemented. The effect of CSDR modelling is investigated over a range of coflow temperatures (Tc) and the stabilisation mechanism is determined from the analysis of the transport budgets and the history of radical build-up ahead of the stabilisation height. For allTc, the balance between chemistry, axial convection, and micromixing, and the absence of axial diffusion upstream of the stabilisation height indicate that the flame is stabilized by autoignition. This conclusion is confirmed from the rapid build-up ofHO2ahead ofH,O, andOH. The inhomogeneous CSDR modelling yields higher dissipation levels at the most reactive mixture fraction, which results in longer ignition delays and larger liftoff heights. The effect of the spurious sources arising from homogeneous modelling is found to be small but nonnegligible, mostly notably within the flame zone.

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Conditional moment closure and large-scale fluctuations of scalar dissipation

Fluid Dynamics ◽

10.1007/bf01050045 ◽

1994 ◽

Vol 28 (5) ◽

pp. 630-637 ◽

Cited By ~ 15

Author(s):

A. Yu. Klimenko

Keyword(s):

Large Scale ◽

Moment Closure ◽

Scalar Dissipation ◽

Conditional Moment ◽

Conditional Moment Closure

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